Two Mathematical Constants

Transcription

1 1 Two Mathematical Constants Two of the most important constants in the world of mathematics are π (pi) and e (Euler s number). π = e = These constants are irrational numbers. You might remember that rational numbers are fractions. When written in decimal form, rational numbers either terminate or repeat. Irrational numbers are nonterminating, nonrepeating decimals. So π and e cannot be written as fractions. Sometimes people approximate π with 22/7. π was discovered in the BC s. e was discovered in the 1600 s. If you take the circumference of any circle and divide it by its diameter, you get π. The constant π is found in geometry, trigonometry, number theory, probability, statistics, topology, Fourier analysis, cosmology, thermodynamics, mechanics, electromagnetism, and so on. x 1 If you take the expression 1 and let x become really big, then the expression gets closer x and closer to e. The constant e is found in calculus, differential equations, probability, statistics, combinatorics, finance, biology, mechanics, electromagnetism, etc. i A formula that contains both π and e is e 1, where i 1. Two Beginning Verses in the Bible The two beginning verses in the Bible are Genesis 1:1 and John 1:1. Genesis 1:1 In the beginning God created the heavens and the earth. John 1:1 In the beginning was the Word, and the Word was with God, and the Word was God. Genesis 1:1 is found in the Old Testament, and John 1:1 is found in the New Testament. Genesis 1:1 was written down by Moses, and John 1:1 was written by the apostle John. Genesis 1:1 was originally written in Hebrew, and John 1:1 was originally written in Greek. In the Hebrew and Greek languages, each letter had a numeric value, as shown on the next page.

2 2 Hebrew Alphabet Name End Form Numeric Value Aleph א 1 Bet ב 2 Gimmel ג 3 Dalet ד 4 Hey ה 5 Vav ו 6 Zayin ז 7 Chet ח 8 Tet ט 9 Yod י 10 Kaf כ ך 20 Lamed ל 30 Mem מ ם 40 Nun נ ן 50 Samekh ס 60 Ayin ע 70 Pey פ ף 80 Tsade צ ץ 90 Qof ק 100 Resh ר 200 Shin ש 300 Tav ת 400 Greek Alphabet Name Upper Case Lower Case End Form Numeric Value alpha Α α 1 beta Β β 2 gamma Γ γ 3 delta Δ δ 4 epsilon Ε ε 5 stigma Ϛ ϛ 6 zeta Ζ ζ 7 eta Η η 8 theta Θ θ 9 iota Ι ι 10 kappa Κ κ 20 lambda Λ λ 30 mu Μ μ 40 nu Ν ν 50 xi Ξ ξ 60 omicron Ο ο 70 pi Π π 80 koppa Ϟ ϟ 90 rho Ρ ρ 100 sigma Σ σ ς 200 tau Τ τ 300 upsilon Υ υ 400 phi Φ φ 500 chi Χ χ 600 psi Ψ ψ 700 omega Ω ω 800 sampi Ϡ ϡ 900

3 3 Genesis 1:1 and π Here is Genesis 1:1 written in Hebrew. It is written from right to left. הארץ ואת השמים את אלהים ברא בראשית There are 7 words with a total of 28 letters. Let s analyze this verse in a table. Hebrew numeric values sum In the beginning 400, 10, 300, 1, 200, 2 בראשית 913 created ברא 1, 200, God אלהים 40, 10, 5, 30, 1 86 the את 400, Heavens השמים 40, 10, 40, 300, and ואת 400, 1, Earth הארץ 90, 200, 1, Now consider this expression: (number of letters)(product of letters) (number of words)(product of words) (28)(23,887,872, 000, 000, 000, 000, 000, 000, 000, 000, 000) (7)(304,153,525, 784,175, 760) (approximation of π times a power of 10) Remember that π , so this is pretty close. The absolute error is less than Sometimes teachers approximate π with 22/ , which is less accurate than the Genesis 1:1 approximation.

4 4 John 1:1 and e Here is John 1:1 written in Greek. It is written from left to right. Εν αρχηι ην ο λογος και ο λογος ην προς τον θεον, και θεος ην ο λογος There are 17 words with a total of 52 letters. Let s analyze this verse in a table. Greek numeric values sum In Εν 5, beginning αρχηι 1, 100, 600, 8, was ην 8, the ο Word λογος 30, 70, 3, 70, and και 20, 1, the ο Word λογος 30, 70, 3, 70, was ην 8, with προς 80, 100, 70, (the) τον 300, 70, God θεον 9, 5, 70, and και 20, 1, God θεος 9, 5, 70, was ην 8, the ο Word λογος 30, 70, 3, 70, Now consider the same expression used in Genesis: (number of letters)(product of letters) (number of words)(product of words) (52)(8,436,251,456,259,110,830, 080, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000) (17)(949,302,241,399,839,184,297,857,869,760, 000, 000) (approximation of e times a power of 10) Remember that e , so this is pretty close. The absolute error is less than I don t see any significance of found in John 1:1 or found in Genesis 1:1.

5 5 Conclusion We see a connection between the two beginning verses in the Bible and two of the most important mathematical constants. Using the same mathematical expression, we saw that Genesis 1:1 gave us π times a power of 10, and John 1:1 gave us e times a power of 10. And 4 both calculations had absolute errors of less than. The constant e was discovered long 100,000 after John wrote down his Gospel, and John would not have known about it. What does this mean? There are a few alternatives. This could be an extraordinary coincidence. Or maybe John studied Genesis without a computer, found π encoded in the first verse, secretly knew about the constant e, and then decided to encode e into the first verse of his Gospel. Or perhaps the Bible is the inspired word of God, and this is just a fingerprint found in the verses. In any case, finding π and e in the Bible is a very intriguing observation. The two foundational beginning verses of the Bible contain mathematics two foundational constants in the order in which they were discovered... and with great accuracy. These discoveries came about as a joint effort involving four people from the UK: Craig Paardekooper, Peter Bluer, Bevan Williams, and Vernon Jenkins.

6 6 You can verify the above findings yourself. Here are some helpful websites Hebrew alphabet Greek alphabet Bible in Hebrew and Greek multiply big numbers Copy and paste the following into Wolfram Alpha to check the calculations. 400*10*300*1*200*2*1*200*2*40*10*5*30*1*400*1*40*10*40*300*5*400*1*6*90*200*1*5 23,887,872,000,000,000,000,000,000,000,000, *203*86*401*395*407* ,153,525,784,175,760 28* /(7* ) ^17 5*50*1*100*600*8*10*8*50*70*30*70*3*70*200*20*1*10*70*30*70*3*70*200*8*50*80*1 00*70*200*300*70*50*9*5*70*50*20*1*10*9*5*70*200*8*50*70*30*70*3*70*200 8,436,251,456,259,110,830,080,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 55*719*58*70*373*31*70*373*58*450*420*134*31*284*58*70* ,302,241,399,839,184,297,857,869,760,000,000 52* /(17* ) ^40